Mathematics, 31.07.2020 14:01 taylorsamodell3217

Look at triangle ABC A (4.5)
5
4
3
2
1
B (2.2)
C (4.2)
1
5 -4 -3 -2 -1 0
1
23
4
5
-1
N
-3
-4
5
What is the length of side AB of the triangle?

A) 3
B) 5
C) square root of 6
D) square root of 13

Look at triangle ABC

A (4.5)
5
4
3
2
1
B (2.2)
C (4.2)
1
5 -4 -3 -2 -1 0
1
23
4
5
-1
N
-3
-4
5
Wh

Answers: 3

Show answers

Answers

Answer from: hbked23

$\sqrt{13}$

Option D is the correct option.

Step-by-step explanation:

Given,

A ( 4, 5 ) , B ( 2 , 2 ) , C ( 4 , 2 )

Let,

A ( 4 , 5 ) → ( x1 , y1 )

B ( 2 , 2 ) → ( x2 , y2 )

Now, finding the length of AB

Use the distance formula to find the length of AB

$= \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$

plug the values

$= \sqrt{ {(2 - 4)}^{2} + {(2 - 5)}^{2} }$

Calculate the difference

$= \sqrt{ {( - 2)}^{2} + {( - 3)}^{2} }$

Evaluate the power

$= \sqrt{4 + 9}$

Add the numbers

$= \sqrt{13}$

Hope this helps..

Best regards!!

Answer from: Quest

5. y=6; de=7; fg=8

6. x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

y = 6

of course, the total chord length is the sum of the lengths of its segments.

de = dh +eh = 3+4 = 7

fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

x = lk = mk×nk/jk = 6×7/10 = 4.2

jl = jk +lk = 10 +4.2 = 14.2

mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

Find the value of the variable and the length of each chord for #5 and #6.

Answer from: Quest

since proposition $p$ states that a number is greater than 25, if $p$ is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted

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Look at triangle ABC A (4.5)
5
4
3
2
1
B (2.2)
C (4.2)

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